The Iconic Math Site
Symbols make common math too difficult. Icons make math easy.
Iconic arithmetic uses the Additive Principle: a sum looks like its parts.
Icons and manipulatives are both formal and friendly.
In binary mode, the Iconic Calculator adds and subtracts by grouping units and merging boundaries.
Decimal Unit Calculator
In decimal unit mode, the Iconic Calculator uses the Additive Principle rather than the Rules of Arithmetic.
Decimal Digit Calculator
In decimal digit mode, the Iconic Calculator uses depth-value notation to add and subtract in parallel.
Unit ensembles add by being put together in the same container.
Depth-value eliminates the stepwise linear sequence of place-value.
Parens express spatial and temporal structure as typographic strings.
Animated container numbers add by merging boundaries and multiply by substitution.
Animated network numbers add by being placed side-to-side and multiply by being placed top-to-bottom.
Iconic form comes in linear, planar and spatial versions. Manipulatives provide physical meaning.
The formal algebra of containers is simpler than the algebra of groups.
Spatial algebra adds by sharing space and multiplies by touching.
James algebra uses three types of boundaries to express all the operations of arithmetic.
Iconic logic provides entirely new ways to think logically.
Boundary logic eliminates duality, converts deduction into deletion, and simplifies critical thinking.
i (the square root of –1) is the multiplicative imaginary. J (the logarithm of –1) is the additive imaginary.
Boolean logic can be expressed by configurations of cubes in space.
Laws of Form
Spencer Brown’s Laws of Form shows us the structure of unary logic.
Boundary logic provides powerful tools for the optimization of semiconductor circuits.
Iconic math is expressed physically by enclosures, blocks, paths, maps, rooms, trees and graphs.
The Principles of Iconic Math apply to many conceptual domains.
By making mathematics humane, iconic math solves some of our problems with math education.